Worker A can complete a certain job in 12 days. Worker B is 60% more efficient than A. In how many days will B alone finish the same piece of work?

Introduction / Context:
Once again we have a comparison of efficiencies between two workers. A has a known completion time for a job, and B is described as being 60 percent more efficient. We need to convert this efficiency relationship into a time calculation and find B's solo completion time for the same job.

Given Data / Assumptions:

• A alone completes the job in 12 days.
• B is 60% more efficient than A.
• Efficiency is measured as work done per day.
• Both workers operate at constant rates.
• Total work is one complete job.

Concept / Approach:
Efficiency and time are inversely related. If B is 60% more efficient, B's rate is 1.60 times A's rate. Given A's time, we find A's daily work rate as 1 / 12. Multiplying this by 1.6 gives B's daily rate. Then we invert this rate to find the time B alone needs to complete the job. This is a straight application of rate and time relationships in work problems.

Step-by-Step Solution:
Assume total work = 1 unit.A's time = 12 days, so A's rate = 1 / 12 work per day.B is 60% more efficient, so B's rate = 1.60 * (1 / 12) = 1.6 / 12.Simplify B's rate: 1.6 / 12 = 16 / 120 = 2 / 15 work per day.Time for B alone = 1 / (2 / 15) = 15 / 2 days = 7.5 days.

Verification / Alternative check:
We can verify with proportional reasoning. A takes 12 days. Since B is 1.6 times as fast, B's time must be 12 / 1.6. Compute 12 / 1.6 = 7.5, which confirms the rate based calculation. Both methods arrive at the same result, giving confidence in the answer.

Why Other Options Are Wrong:
Eight days would correspond to a smaller increase in efficiency than 60%. Six point four days or 5.5 days indicate significantly higher efficiencies than the stated 60% increase and do not match the specified relationship between A and B. Only 7.5 days is consistent with B being exactly 60% more efficient than A.

Common Pitfalls:
Students sometimes misinterpret 60% more efficient as meaning B takes 60% of A's time directly, which would imply a different efficiency factor. Another issue is performing decimal division incorrectly when computing 12 / 1.6. To avoid errors, it is often easier to work with fractions, for example, 12 / (8 / 5) = (12 * 5) / 8 = 60 / 8 = 7.5 days.

Final Answer:
B alone can complete the job in 7.5 days.